Colloidal
suspensions are widely used to study fundamental problems in condensed matter
physics since they behave in many aspects like model atomic systems, exhibiting
liquid, crystal and glassy phases. For hard interparticle interactions, these
phase changes are achieved by tuning the particle volume fraction, f, which is the only independent thermodynamic variable
in this case. For more general interparticle interactions, these phase changes
can also be achieved by changing either the range or the strength of the
interaction. Interestingly, the intrinsic softness of microgel particles, which
are colloidal-size, crosslinked polymer networks, can also have important
effects over the suspension phase behavior; for instance, Senff and Richtering
found that crystallization and melting occurred at higher volume fractions and
exhibited a narrower phase coexistence region compared to hard sphere
suspensions. Furthermore, particle softness can also affect kinetic arrest and
hence the liquid-to-glass transition; Mattson et.al. recently found that while
hard microgel suspensions behave like fragile molecular glass formers,
suspensions comprised of soft microgels exhibited a behavior reminiscent of
strong molecular glass formers.

While there is evidence
that particle softness affects the phase and non-equilibrium behavior of the
suspension, the physical scenario behind such influence remains largely
unknown. This, in part, results from the lack of an adequate way to think about
particle softness. Indeed, one could think about softness in terms of the
interparticle potential, which would exhibit a soft repulsion for
center-to-center distances below the particle diameter. Alternatively, one
could think about softness in terms of a relevant elastic modulus of the
particle or even in terms of internal degrees of freedom, since these
contribute to the thermodynamics of the suspension. We have performed work to
unravel this puzzle and to elucidate the way particle softness affects the
suspension behavior.

We have employed three
classes of microgel particles. The first one consists of vinylpyridine, a weak
base that ionizes at low pH, and divinylbenzene (DVB), a crosslinker. This
particle was used to understand the influence of particle stiffness, which we
tuned by using different amounts of DVB, over the suspension phase and
non-equilibrium behavior. We always worked at a constant pH of 3, where the
particles are fully swollen. For stiff microgels, the suspension exhibits
liquid, crystal and glassy phases. This is reminiscent of hard sphere behavior.
However, for our microgels, we find that the width of the liquid-crystal phase
coexistence region increases as the DVB concentration decreases. We believe
this results from the influence of the microgel internal degrees of freedom that
can contribute to the entropy of the system and hence to the particle
concentration jump involved when the liquid phase transform into the crystal
phase. For softer microgels, we observe that the suspension does not
crystallize. Instead, there is a glass transition at certain particle
concentration. But even more remarkably, for even softer microgels, the
suspension remains liquid irrespective of the concentration. Overall, these
results emphasize the rich phenomenology that can be brought about when the
particles are deformable and compressible as opposed to being rigid and
non-interacting.

The second class of
microgel particles consists of poly-(N-isopropylacrylamide), pNIPAM, a
thermosensitive polymer, acrylic acid, a weak acid, and the crosslinker methylene-bis-acrylamide
(BIS); these particles change size in response to temperature and pH changes.
The suspension size distribution has a width of 12% of the mean. With this
system we focused on the crystal phase and did extensive Small Angle Neutron Scattering
to determine the suspension structure factor. We then compared the experimental
results with the expected structure factor of well known crystal structures and
found that the agreement was best for suspension polydispersities that were
less than that measured in dilute conditions. These results suggest that the
suspension phase behavior can rely on polydispersity changes. For hard spheres,
crystallization is driven by the increase in entropy that results from the gain
in free volume per particle. For soft, deformable objects, this entropy gain competes
with the entropic penalty associated to changing the preferred equilibrium size
of some microgels to reduce the suspension polydispersity. For sufficiently
soft particles, this entropy penalty might be smaller than the entropy gained
by crystallizing and as a result these suspensions will change their
polydispersity to allow the system to crystallize. We have recently synthesized
large batches of microgel suspensions with different average sizes to make
suspensions with home-made size distributions. This will allow us to test this
hypothesis and understand the apparent polydispersity change in the crystal
phase with respect to the dilute situation.

The third
type of microgel particles also consists of pNIPAM,
but it is crosslinked with poly(ethylene glycol diacrylate), PEG, which is a
hydrophilic polymer. Particles based on pNIPAM appreciably deswell at a lower
critical solution temperature (LCST) of approximately 305 K; it is the change
in solubility around this temperature which is
responsible for this behavior. A major problem
is that pNIPAM microgels aggregate and eventually gel at temperatures above the
LCST; the change in solubility responsible for particle deswelling also induces
the required interparticle attraction for the suspension to become colloidally
unstable. This hinders exploring the influence of swelling alone over the
suspension phase behavior, as changes in temperature change the interparticle
interactions from repulsive at low temperature to attractive at high
temperatures. By using PEG as cross-linker, the repulsion is maintained
beyond the LCST. It is the hydrophilicity of this polymer which, at high
temperature, segregates towards the periphery of the particles to assure the
desired repulsion. Our aim is to use these particles to explore how the
swelling degree and hence the stiffness of pNIPAM microgels affects glass
formation. At this point (i) we have performed a detailed light and neutron
scattering characterization of the particles to understand how the microgel morphology
changes with temperature, and (ii) we have exploited the colloidal stability of
the suspension to measure how the bulk modulus of the particles changes through
the swelling transition. Consistent with what was found for pNIPAM macrogels,
the bulk modulus of our microgels drops at the LCST.